Monetary and Fiscal Policy Interaction

Quantitative and Qualitative Analysis in Social Sciences Volume 4, Issue 2, 2010, 82-113 ISSN: 1752-8925

Monetary and Fiscal Policy Interaction: What is the Role of the Transaction Cost of the Tax System in Stabilisation Policies? Panagiotis Chronisa

Aspassia Strantzalou

Bank of Greece

Ministry of Labour and Social Insurance, Greece

Abstract Allowing fiscal policy to affect households’ behaviour when imposing taxes, can be viewed as a transaction cost of the tax system. In the light of the underlying state-taxpayer interplay, we study monetary and fiscal policy interactions in a two-country framework of a monetary union. This paper evolves in two directions. First, we endogenously derive (within optimality) the functional form of the transaction cost. Second, we investigate the constraints that this cost (endogenously) imposes on the efficiency of fiscal policy. This way, we develop a channel through which fiscal policy is related to price stability, the primary objective of the Common Central Bank (CCB), via the concept of the transaction cost of the tax system. Furthermore, within this framework, we investigate the effectiveness of fiscal rules (like the European Union Stability and Growth Pact) in building sound fiscal policies and maintaining price stability. JEL Classifications: E52, E58, E62, E63, H60. Keywords: Monetary policy, fiscal policy, transaction cost, tax system, stability and growth pact.

Acknowledgements: We thank V. Droucopoulos, H. Gibson and Y. Stournaras for their helpful comments. All remaining errors are ours. The views expressed in this paper are those of the authors and do not necessarily reflect the views of the Bank of Greece nor the Greek Ministry of Labour and Social Insurance.

a

Corresponding author. Economic Research Department, Bank of Greece, 21 E. Venizelos Ave. Athens 102 50, Greece; tel.: +30 210 3202368, email: [email protected]

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1

Introduction

In the theory of monetary and fiscal policy interactions, the assumption of Ricardian households isolates fiscal policy aspects from the determination of equilibrium. The nondistortionary (lump-sum) taxation assumption, in the majority of these models, abstracts from the need to analyse the effects of fiscal instruments, resulting in the neutrality of fiscal policy. Thus, monetary policy, as described by the Taylor rule,1 plays a deterministic role in equilibrium, increasing the importance of the monetary policy parameters. Hence, neither debt dynamics nor the endogenous effects of the fiscal instruments, play a role in determining equilibrium, implying fiscal policy neutrality with respect to inflation. By contrast, when one deviates from the assumption of Ricardian equivalence and turns to a distortionary system of taxation, then the inflationary consequences of fiscal policy have to be examined. Edge and Rudd (2007) show that the coefficient on inflation in the Taylor rule depends positively on the tax rate, indicating non-neutrality of fiscal policy. In the context of distortionary taxation, fiscal policy affects households’ behaviour, macroeconomic variables (such as income, via the income and substitution effects, consumption, etc.), and, in a dynamic way, the effectiveness of fiscal instruments. Thus, by relaxing the assumption of non-distortionary lump-sum taxation, we let fiscal policy have an endogenous effect on fiscal deficits and the debt path, generating inflationary consequences. The literature discusses the non-neutrality of fiscal policy in an asymmetric way2 by using either ad hoc policy rules in a stochastic environment, or a proportional tax system in a general equilibrium framework. As Leeper and Yun (2006) mention, “although instructive for some purposes, the assumption that all taxes are lump-sum prevents the fiscal theory from being understood in the context of the broader public finance”. The analysis becomes more interesting when one considers the question of monetary and fiscal policy interactions in a monetary union, like, for example, EMU, with different countries and a single central bank. It is then possible for each country’s fiscal policy to have spillover effects on price stability. Such effects are validated for the euro area by

1

See Taylor (1993). See, for example, Leeper (1991), Woodford (1994), (2001), (2003), Benhabib, Schmitt-Grohe and Uribe (1997, 2004), Leeper and Yun (2006), Schabert and von Thadden (2009).

2

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simulation results: for example, an increase in Germany’s public expenditures by 1% of GDP increases the (common) inflation rate by 0.4%.3 In this paper, we deviate from the homogeneity assumption used in the majority of the literature, and we analyse monetary and fiscal policy interactions in a monetary union of heterogeneous countries. Within this framework, our main contribution is the introduction of the operation or transaction cost of the tax system into economic (monetary and fiscal) policy analysis. This way, we allow fiscal policy to endogenously affect (via the transaction cost) the price stabilisation policies of the Common Central Bank (CCB), thus resulting to the non-neutrality of fiscal policy. The idea of this transaction cost (see also Jrbashyan and Harutyunyan, 2006) is similar to the notion of a transaction cost that appears in other market activities. It comprises tax collection (Barro, 1979), tax evasion (Allingham and Sandmo, 1972), Feinstein, 1991) and tax compliance (Clotfelter, 1983; Andreoni, Erard and Feinstein, 1998), all closely related to the behaviour of different types of tax-payers that give rise to the state–tax-payer interaction. The paper is organised as follows. Section 2 builds and presents the model. Section 3 solves the optimisation problems and gives the optimal policies that each country and the central banker should adopt. Section 4 analyses the transaction cost of the tax system, and derives the optimal reply functions of each country and the response of the CCB. Section 5 discusses economic policy using two scenarios regarding the asymmetry/symmetry of the countries with respect to their tax system’s transaction cost function. Section 6 examines the effectiveness of numerical fiscal rules in the presence of the transaction cost. Finally, Section 7 concludes.

2

The Model

We build a model with two types of countries: those with a debt level above their reference value (debtor countries) and those with a debt level below their reference value (non-debtor countries). For simplicity and without loss of generality, our economy consists of two countries, a debtor and a non-debtor one, and the central bank.

3

See the Quarterly Report on the Euro Area, vol. 6 (2), European Commission, 2007.

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Within each country, we assume that there exists a society, whose decision to re-elect the government is the result of the solution to an optimisation problem. Thus, in our economy, we have three agents: society, government and the central bank.

2.1

Society

Society has preferences over consumption and public goods, which are described by a loss function. Its aim is to minimise this loss function. The minimisation procedure raises the issue of whether society should optimally re-elect the existing government or not, since it is the government’s (policy) choices that determine, up to a point, its loss function. Specifically, the society in each country has preferences over consumption (C) and public expenditure (G). These preferences are described by a loss function, Ls , of the form Ls = – C2 – β.G2

(1)

with C = W -T, where W stands for the wage and T for tax levels. Assuming W =1, we can write: C = 1 – T.

2.2

(2)

The Governments

As far as the government of each country is concerned, we deviate from the usual assumption of the benevolent dictator, assuming that it cares about the operational cost of its fiscal policy decisions. It produces public goods by issuing debt and by collecting taxes, facing a transaction cost. The government wants to be re-elected; its re-election depends on the probability of no re-election, P, which is discussed in more detail later. Hence, the government cares about its probability of (no) re-election.4 Governments choose their tax policies (tax rates) aiming at minimising their loss functions. In particular, each government’s preferences are described by a loss function that depends on the transaction cost of the tax system, on public expenditure, and on the probability of no re-election (or, equivalently, the cost of not being re-elected)5. 4

It is worth noting, that this self-interest characteristic of the government is consistent with its interest in the frictions created by its policy choices. 5 See equation (4) below.

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More specifically, in our analysis we allow for a monetary union (MU) between two countries: the first, country i, has a debt level, expressed as a percentage of its GDP, greater

()

than a reference value b , i.e. bi > bi .6 The second, country j, has joined the MU with a debt level less than or equal to its reference value, that is, b j ≤ b j . For simplicity, let the reference debt value be the same for both countries, i.e. let bi = b j = b . The transaction cost of the tax system corresponds to a micro characteristic of public finance, reflecting the distortionary character of the tax system. Our aim is to enter this into a monetary and fiscal policy interaction model, in order to endogenously investigate, via a microfoundation setting, how the distortions generated by fiscal policy affect the macroeconomic variables within the MU and the conditions under which this takes place. The imposition of taxes generates frictions due to state–tax-payer interactions. These frictions relate the behaviour of tax-payers, stipulated by economic, sociological and psychological characteristics, to tax administration aspects, like tax collection and tax compliance, thus resulting in a loss of tax revenue, with budgetary consequences.7 Since the effect of the marginal tax rate on tax-payers’ behaviour is not controversial in fiscal theory, we consider the transaction cost of the tax system as a function of the tax rate. Following Barro (1979), we assume the operational cost of the tax system (Zt) to be equal to the net tax collections (T) multiplied by a function ( f ) of the tax rate (τ), i.e. the transaction cost function is Z=T . f(τ). However, we deviate from Barro by not pre-assuming the properties of Z and f, but by endogenously deriving their properties from the optimal solution of the model. The only plausible assumption made is that f ΄>0, reflecting the notion of the operational cost due to the existence of the tax rate. As a logical consequence of the above and, since the marginal tax rate is the source of frictions between state and tax-payers, the government’s fiscal policy, as implemented through the tax instrument, affects the households’ opinion (satisfaction or not) of the government. If one assumes that the government wants to be re-elected by the households, then such dissatisfaction entails a cost for the government. In our analysis we assume that this cost enters the governments’ preferences; in other words, we assume that each government cares about the effect of its policies on households’ welfare.

6

We use capital letters to express the magnitude of a variable X and small letters to denote its rate, i.e. the variable X divided by the GDP (Y): x= X/Y. 7 Clotfelter (1983) notes that in 1976 the unreported income in the US was $75 to $100 billion, or 7% to 9%, of reported income.

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More specifically, we assume that the exact effect of society’s perception of the government’s policy choices is embodied in a function Φ of the form:

R| 1⋅ L Φc L h = S P ⋅ L |T0 ⋅ L = 0 s

s

s

S

, , ,

L < Ls L < Ls < L, P ∈ 0,1 , LS < L

b g

(3)

where P stands for the probability of no re-election, L and L are the critical values for the society’s loss. If the actual loss exceeds L , then the government is not re-elected (with probability P =1); if the loss is below L , then the government is re-elected for sure (i.e. P =0), while it is P ∈ (0,1), whenever the society’s loss is between L and L . Thus, the way the society’s loss function ( LS ) affects the government’s objective function is determined by the way changes in LS affect the society’s willingness to vote for the government. We use the exogenous probability of no re-election, P, as a measure of this willingness. Specifically, we assume that P corresponds to real numbers in such a way that a high number is always related to high values of the society’s loss function ( LS ). Intuitively, this implies that the unsatisfied society, i.e. a society with a high loss function, is less likely to re-elect the government, and hence P is high. Hence, the society’s loss function affects the government’s loss function to the extent that the probability of no re-election indicates and it should, therefore, be included in the government’s loss function. So, the government’s loss function can be written as:

LG = Z 2 + ξ ⋅ G 2 + P ⋅ LS ,

(4)

where G stands for the public good. The term Pi ⋅ LiS captures the exact effect the society’s loss function has on the government’s objective function. With the appropriate rearrangements, the above loss function can be written8 as: LG = Z 2 − ( P β − ξ ) ⋅ G 2 − P ⋅ C 2 .

(5)

Thus, in a two-country world,

b

g

Li = Zi − Pβ − ξ ⋅ Gi − P ⋅ Ci G

2

2

2

(5.i)

corresponds to the objective function of country i’s government and

Notice that if P > ξ/β then the government’s loss reduces with an increase in the public expenditures, reflecting the characteristics of a myopic government that is most likely not to be re-elected (Alesina, 1990; Alesina and Tabellini, 1987; Cukierman and Meltzer, 1989; Tabellini and Alesina, 1990; and Rogoff, 1990). ξ On the other hand when P < /β (i.e when there is no political uncertainty) an increase in expenditures implies a budgetary cost for the government.

8

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b

g

L j G = Z j 2 − Pβ − ξ ⋅ G j 2 − P ⋅ C j 2

(5. j)

is the objective function of country j’s government. In our analysis, we delve into deriving conclusions about the effectiveness of fiscal rules when the countries are heterogeneous within the MU. The role of the budget constraint is vital for this investigation. Crucial for such a budget constraint is the way the fiscal rules enter and affect the countries of our economy, both the debtor and the non-debtor country. Following Beetsma and Uhlig (1999) and Debrun (2007), and since fiscal rules constitute an inhibitory mechanism for governments to accumulate public debt beyond a certain threshold b , we introduce the cost for breaching this threshold. One way of approaching this cost is by considering it as a numerical fiscal rule (for example, the Stability and Growth Pact, SGP) that corresponds to utility or budgetary losses for policy makers, when they deviate from the rule.9 However, in the case of numerical fiscal rules, these losses for the breaching (debtor) country are assumed to be distributed among the other (non-debtor) countries of the MU, implying budgetary gains for them. Additionally, we define δ ∈ (0, 1) as the degree of austerity for deviating from the rules. Thus, the term δ ( bi − b ) shows the loss for the debtor country (with bi > b ), or, equivalently, the gain for the non-debtor country. Alternatively,

d

i

δ bi − bi stands for country i’s cost of breaching the threshold of this reference value. More specifically, the recourse constraint for the debtor country takes the form: 10

d

c

i

h

Yt i + Bti − δ Bi − B i = Gti + Bti−1 1 + π e − π ⇒

d

i

c

h

Gti = Yt i − δ Bi − B + Bti − Bti−1 1 + π e − π . Dividing by the country’s national income at time t, Yt i , we get:

gti = 1 − δ ( bi − b ) + bti − bti−1 (1 + π e − π ) ,

(6)

where πe and π are the expected and actual levels of inflation, respectively, and bti−1 is the amount of debt issued by the government and traded in the market in the preceding period. Following Beetsma and Uhlig (1999) we assume that the real world market interest rate is zero. In order for risk neutral agents to be willing to hold government bonds the expected 9

This can be consistent with Article 104c of the Maastricht Treaty, where the cost for deviating from the rules (i.e. for having a debt level greater than 60% of its GDP) is set to be a non negligible amount of GDP. 10 Recall that bi > b for country i.

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rate of return, πe, includes a mark-up equal to the expected inflation rate. The ex-post real rate of return is given by πe – π. For the non-debtor country, j (whose debt level is below its reference value), the resource constraint captures the idea that following sound fiscal policies results in a gain within the above-mentioned redistribution among the countries. 11 These constraints can be written as

d i + δ d B − Bi + B

c c1 + π

h −πh ,

Yt j + Bt j + δ Bi − B i = Gt j + Bt j−1 1 + π e − π Gt j = Yt j

i

t

j

− Bt j−1

e

where, dividing by Yt j , we get the way the government finances its expenditures.

d

c

i

h

gtj = 1 + δ bi − b + bt j − bt j−1 1 + π e − π .

(7)

Summarising, the problem the government of each country (i, j) faces, can be written as:

b

g

min LGi = ( zti ) 2 − Pβ − ξ ( gti ) 2 − P(cti ) 2 bi ,τ i

d

c

i

s.t gti = 1it − δ bi − b + bti − bti−1 1 + π e − π

h

Z

with z = /Y , and

b

g

min LGj = ( ztj ) 2 − Pβ − ξ ( gtj ) 2 − P(ctj ) 2 b j ,τ

j

d

i

c

h

s.t. gtj = 1 + δ bi − b + bt j − bt j−1 1 + π e − π . Obviously, δ = 0 corresponds to the case where there exists no numerical fiscal rule.

2.3

The Common Central Bank

The common central banker is appointed in order to carry out price stabilisation policies. He takes into account the total debt level and derives the optimal inflation rule to follow, for any given fiscal policies. This implies that the central banker may also be aware of the constraints that unsustainable public finances impose on the monetary policy rule, which is consistent with the non-Ricardian regime of our analysis, reflecting how aggregate demand and supply, including the effect of fiscal policy, affect price stability. On the other hand, in

11

An alternative way of approaching this is to think of δ ( bi − b ) as the level of the penalty, imposed on the

debtor country, for deviating from the debt rules and distributed among the other countries.

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our model the rate of inflation works as an interest rate, with its changes affecting the debt level for each country (and hence the total debt for the MU). The above allow us to write the MU’s total debt level as a function of the inflation rate ~ π, i.e. b π . So, it is logical to assume that the CCB has preferences about inflation and the

bg

fiscal constraints described by the path of the total debt at MU levels.12 The CCB’s objective is to determine the (common) inflation level, which is consistent with its stabilisation policies. This objective is described by a loss function of the form:

(

)

2 LCCB = γ b (π ) + θπ 2

b g

~ ~ with γ, θ ∈ 0,1 and where b stands for the total MU debt, i.e. b = bi + b j . The problem the CCB faces can be written as

(

)

2 min LCCB = γ b (π ) + θπ 2 .

π

3

Solution

We solve the above optimisation problems as a simultaneous equation problem. We look for the optimal policies that each country and the central banker should adopt in order to minimise their losses. Within this framework, we also consider the constraints imposed on the efficiency of fiscal policy through the transaction cost of the tax system, and the way this is related to the political cycle. The existence of a transaction cost captures the fact that, before tax-payers are called upon to pay taxes, they have already weighed up their gains and losses from this procedure and they decide, accordingly, on the degree to which they will comply with fiscal rules. This relationship between tax-payers and the state (represented, in each time, by the governing political party) is a direct implication of the tax system that creates frictions. It is these frictions that govern the magnitude of the transaction cost and, eventually, circumscribe the efficiency of fiscal policy, putting pressure on the CCB’s price stabilisation policy.

12

See also Van Aarle, Bovenberg and Raith (1997), Beetsma and Uhlig (1999), Chari and Kehoe (2007), and Nguyen and Kakinaka (2006).

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This way, we describe a mechanism through which each country’s fiscal policy within the MU interacts with the CCB’s monetary policy, where optimality depends on the microeconomic characteristics of fiscal policy. The first order conditions for the government of country i’s maximisation problem, are:

)

(

∂LGi = 0 ⇒ zi fi + τ i ⋅ f i′ = ( β ⋅ Pi − ξ ) gi − Pi ⋅ ci , ∂τ i

(8)

and

∂LGi = 0 ⇒ 1 + (1 − δ ) bti − ci + δ b − bti−1 (1 + π e − π ) = 0 . ∂bi For country j, the first order conditions require that ∂LGj ∂τ j

c

h c

h

= 0 ⇒ z j f j + τ tj ⋅ f j′ = β ⋅ Pj − ξ gtj − Pj ⋅ ctj

(9)

(10)

and ∂LGj ∂b j

= 0 ⇒ 1 + bt j − c j + δ ( bti − b ) − bt j−1 (1 + π e − π ) = 0

(11)

From equations (8) and (10), we can easily derive (since f ΄>0 for both i and j) the probability of no re-election for any country: P>

ξ ⋅g β ⋅g −c

.

(12)

This proves that the existence of the tax system is consistent with frictions, reflecting the state–tax-payers’ interaction, which is not independent of households’ preferences, as these are expressed by the government’s re-election. This is also justified by the existence of the political cycle. The first order condition for the CCB’s optimisation problem gives the optimal inflation rule: ∂LCCB ∂b θ =0⇒ = − ⋅ π ⋅ b −1 (π ) . γ ∂π ∂π

4

(13)

Analysis

4.1 The Transaction Cost of the Tax System In this section we carry out a theoretical investigation of the way the transaction cost of the tax system (expressed as a percentage of GDP) is related to the tax rate and we endogenously derive the properties of the transaction cost function. 91

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From the fist order conditions (8) and (10), it can be shown that in each country at time 13

t:

( ft + τ ft′) =

1 ⎡( β P − ξ ) gt − P ⋅ ct ⎤⎦ . zt ⎣

(14)

The transaction cost is described by the function z = τ .f(τ). Differentiating with respect to τ gives the first order derivative of the function z:

∂z = f + τf ′ which shows the way ∂τ

b

g

the transaction cost changes with the tax rate. The second order derivative of this function,

z΄΄(τ), alternates sign and so the transaction cost function z(t) exhibits an inflection point at

c z , τ h = c P ( β ⋅ g − c ) − ξg , τ h . *

*

*

As a result, the operation cost of the tax system is related, in a non-linear way, to the tax rate, as can be seen from Figure 1. Moreover, from this figure, it is obvious that the transaction cost of the tax system (and hence the frictions as well) increases at a diminishing rate for tax rates less than τ*, while it increases at an increasing rate, for tax rates greater than τ*. Rearranging equation (14) gives 1 ⎡ P ( β ⋅ gt − ct ) − ξ ⋅ gt ⎤⎦ , (14.a) zt ⎣ which shows that society’s reaction to the government’s economic policy choices (as this is

( ft + τ ft′) =

reflected in the probability of no re-election, P), affects the rate of change of the transaction cost of the tax system (ft + τ f΄t). Consequently, the political cycle is related to the government’s choices and to the endogenous way in which the efficiency of the fiscal policy works, thus embodying households’ preferences as these are shaped by the welfare implications of the government’s fiscal policy. In an attempt to qualitatively represent the frictions that fiscal policy creates, as a result of the state–tax-payer relation, we describe in the sequel the exact way the political cycle is related to the tax system’s transaction cost: Figure 2 shows that when the change in the transaction cost, as a result of the government’s choice to increase the tax rate, is relatively small, then the government’s probability of no re-election is reduced. The economic, sociological and psychological aspects of fiscal policy choices that reflect the households’ behaviour are related, via the probability of no re-election, to the political cycle and the way this affects the government’s

13

For the moment, we abstract the lower case country indices (i, j).

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economic choices, given that it cares about the political cost (re-election or not) of these choices. Figure 1

The Operation Cost of the Tax System as a Non Linear Function of the Tax Rate

z f(τ) zf

z(τ)

z*

τ*

τf

τ

Figure 2

Changes in the Probability of no Re-election along the Transaction Cost Function

z

z*

P τ0

P

P τ1

τ

Thus, when the government chooses to increase the tax rate within the range [τ0, τ1] the increase in the tax system’s transaction cost is relatively small and is related to an efficient fiscal policy, since it is consistent with small frictions. The probability of no re-election decreases within this area and, hence, the government is more likely to be re-elected. When the government chooses tax rates higher than τ1, the operation cost of fiscal choices increases resulting in inefficiencies. The state–tax-payers’ interaction is more likely to be characterised by large frictions and has a political cost, since the probability of no reelection increases. 93

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In Figure 2 we can observe that the probability of no re-election (seen as an indicator of people’s dissatisfaction with the government’s tax policy) also rises for very small tax rates. This, within optimality and in the context of our analysis, corresponds to an area of tax rates close to zero, where the transaction cost function is very inelastic,14 indicating that small increases in tax rates are consistent with very high rates of growth of the transaction cost. This is in line with the logic of our model and the notion of transaction cost. In other words, it describes society’s dissatisfaction (an indicator of which is the probability of no re-election, P) when, from a world of no taxes (i.e. zero tax rates) the government starts imposing taxes (i.e. positive tax rates). However, here we do not go into the details of this case since, as real world practice indicates, the tax rates chosen by fiscal authorities are not negligible. Hence, our analysis focuses on tax rates greater than τ0.

4.2

Reply Functions

In this section we derive the optimal reply functions for each country, which depict the way each country’s fiscal policy interacts with that of the other, through the constraints imposed by the independent CCB’s monetary policy. This is done by combining the first order conditions of the optimisation problems previously described. More specifically, these reply functions are derived from the first order conditions (9) and (11) of the countries’ problems and the optimal inflation rule, as this is defined by the first order condition (13) of CCB’s problem. Assuming rational expectations, we derive the optimal reply functions for each country. The reaction function bij (bi ) = bijt for country i is

bijt =

b g

1 − ci + δb − 1 + π b ~ γ ∂b i b θ ∂π t −1

i t −1

+

b g

1− δ −

~

γ ∂b i b θ ∂π t −1 bi . ~ t

γ ∂b i b θ ∂π t − 1

(15)

Similarly the reaction function b jj (bi ) = b jtj for country j is

14

lim ( f + τ f ′ ) = lim+

τ → 0+

τ →0

P ( βγ − c ) − P Y = = −∞ z 0

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~

γ ∂b j j bt −1 δ− − c − b − + b 1 δ 1 π j t −1 j ∂ θ π bti . b jt = − − ~ ~ γ ∂b j γ ∂b j bt −1 b 1− 1− θ ∂π θ ∂π t − 1

b g

(16)

Both optimal reply functions are negatively sloped with slope of bij (bi ) < slope of b jj (bi ) .

These properties of the loci are depicted in Figure 3.

Figure 3

The Reaction Functions bj bij (bi )

b jj (bi )

bi

Note that these reaction functions encapsulate the way the microeconomic characteristics of fiscal policy, due to the frictions of the tax system’s transaction cost, are related to the political cycle and the monetary policy of the independent CCB. The equilibrium is determined by the intersection point of the two reaction functions. This will be derived by simultaneously solving equations (15) and (16), which gives: bj =

β Pj − ξ Pj

gj −

z j ( f j + τ j f j′) bt j−1 ⎡ β Pi − ξ z ( f + τ f ′) ⎤ b δ bi + (1 − δ ) bt j−1 b j − bi − i ⎢ gi − i i i i ⎥ + ti−1 δ b + t −1 i t −1 − t −1 i bi . Pj bt −1 ⎣ Pi Pi bt −1 bt −1 ⎦ bt −1

(17) Expression (17) provides a rule for the path of the economy, since it characterises all the intersection points of bij (bi ) and b jj (bi ) , for any given level of π and τ (see Figure 4). 95

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Figure 4

Representation of the Economy’s Total Debt bj b ij ( bi )

b ( bi )

b jj (bi )

bi

Notes: The representation of the economy’s total debt, as determined by the intersection point of the countries’ reaction functions.

4.3

CCB’s Response

The Common Central Banker is independent. His only objective is to use his policy instrument, the interest rate, in order to keep inflation below or equal to a reference value,15 under the constraints imposed by the fiscal policies of the country members. This implies a relationship between the two countries’ fiscal policies (as described by the level of total MU ~ debt, b ) and price stability (which is the CCB’s objective).16 As shown in equation (13), in the context of optimisation, monetary and fiscal policies are related as follows: ∂b θ = − ⋅ π ⋅ b −1 (π ) . γ ∂π 15 16

In the case of the EMU this could be less but close to 2%. See equations (6), (7), (15), and (16).

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~ We look at the above relationship, as the first order derivative of a function b (π), which describes the CCB’s best response to changes in total debt within the MU. Its second ~ ∂ 2b derivative requires that, at the minimum loss, < 0 . Hence, we have endogenously ∂π 2 ~ derived the properties of a function b (π), which shows the CCB’s optimal response to the fiscal outcome and the effect this response has on total debt. The above are described in Figure 5. Figure 5

CCB’s Optimal Response to the Fiscal Outcome ( b ) b

b (π )

π

 Since the first order derivative ∂b

∂π

, as described by equation (13), is a function of

~ inflation, π, the value of the total debt within the MU ( b ) will depend on the level of inflation. That is, whenever inflation changes, the MU’s total debt is affected and this is ~ shown by moving along the line b (π). This is because a tight monetary policy by the CCB increases the ex post real rate of return, πe – π, and, hence, the debt level for each country member via the term (1+πe-π)bt-1 of their budget constraint. Woodford (2003) notes that “… monetary policy (the choice of it ) affects the evolution of the public debt, even in the absence of seignorage revenues, through its consequences for debt service on existing government debt. In most advance economies, this is actually the most important fiscal consequence of monetary policy …”. 97

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~ Furthermore, the shape of the b (π) function, as well as the economic interpretation of this shape, is along the lines of King’s (1995) analysis. He uses the expression “some unpleasant fiscal arithmetic” to describe the effects of the central banker’s disinflationary policies on the debt dynamics.

5

Economic Policy

In this section we aim at making economic policy inferences. For this, we will combine the properties of the above-mentioned transaction cost and the constraints it imposes on the efficiency of fiscal policy with the derived reaction functions of the country members and the CCB. This way, we will be able to determine the debt path for each country separately, as well as the path of total debt (for the MU). This procedure will also enable us to specify the optimal trajectory of our economy, which is not independent of the CCB’s optimal policy (as this is formally explained by its reply function), thus implying the existence of second order effects. Because the degree of the countries’ homogeneity is a determining factor of the whole economy’s path, in what follows we study our economy under different scenarios regarding the countries’ transaction cost level, as this cost is assumed to be the main factor of homogeneity. Hence, we can study the constraints it imposes on the countries’ strategic behaviour and the way this is related to the political cycle. We can categorise our scenarios into two groups. The first consists of the cases where the countries face considerably different levels of transaction costs, or equivalently, where they lie within different ranges of the transaction cost function z. Within our framework, this is the most “realistic” scenario.17 The second scenario includes cases where the countries (although heterogeneous regarding, for example, their initial debt conditions) face similar transaction costs, that is, they both lie within the same range of the transaction cost function z. We show that when we have a considerable degree of heterogeneity, the tax system’s transaction cost is the factor determining the countries’ policy choices and hence, the resulting level of debt and its inflationary consequences. On the other hand, when we have a

17

This also applies to the EMU case of heterogeneous countries (as this is signified by the existence of fiscal rules, like the Stability and Growth Pact).

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considerable degree of homogeneity, it is the countries’ strategic behaviour that determines the outcome.

5.1

Scenario 1: Asymmetric Countries, with respect to their Tax System’s Transaction Cost Function

When fiscal authorities choose tax rates that differ considerably from each other, corresponding to different levels of costs on the transaction cost function, then the countries face different properties regarding their tax system’s transaction cost and, consequently, they are associated with different efficiency levels of their fiscal/tax policies. So the (initial) heterogeneity of the countries results in a different outcome for the economy, depending on which country (the initially better-off or not) has set higher tax rates. We therefore assume that each country increases its tax rate and we examine the economy’s outcome in the following cases.

5.1.1

Case 1.1: Debtor country (i) introduces lower tax rates than the non-debtor one

Country i has a relatively lower rate of increase in its transaction cost than country j due to each unit increase in the country’s tax rates.18 This, makes country i’s tax instrument more efficient in raising finance in order to serve the debt. Within optimality,

ξ g i + zi ( f + τ f ′ ) i ∂CTi =− > 0, ∂Pi γ ∂b i 2 b P θ ∂π t −1 i

(18)

where CTi stands for the constant term of country i’s reply function. This suggests that any increase in Pi (as a result of a government’s attempt to increase tax rates in order to finance the country’s debt) 19 would shift the bij (bi ) locus backwards from bij (bi ) 0 to bij (bi ) 1, reducing the country i’s debt level.

18

An Appendix with the details of the transaction cost function z is available from the authors. Recall that, as shown in equation (14a), the rate of change in the transaction cost is monotonically related to the society’s dissatisfaction which is captured by the probability of no re-election.

19

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Country j, chooses high tax rates, being situated at the right end of the transaction cost function, where the rates of change are high, pointing to high frictions. This means that the tax-payers’ dissatisfaction, caused by the welfare implications of any increase in tax rates is high, and hence the probability of no re-election is also high. In this case the government’s tax instrument is inefficient in serving country j’s debt. Within optimality, it is ∂CT j ∂Pj

=

ξ g j + z j ( f + τ f ′) j ⎛ γ ∂b j ⎞ 2 bt −1 ⎟ Pj ⎜1 − ⎝ θ ∂π ⎠

< 0,

(19)

where CTj stands for the constant term of country j’s reply function. Any increase in country j’s tax rates would moderate society’s welfare, driving up the government’s probability of

no re-election. Consequently, the b jj (bi ) locus shifts upwards, from b jj (bi ) 0 to b jj (bi ) 1, causing country j’s debt level to rise. This is pictured in Figure 6.

Figure 6

bj z

2

b j1

z(τ) 1

bi 2 bi1

b j2

b1

0

b0

bi 0 b j 0

country i

b2

bi

country j τ

b

π

Notes: The path of the economy when the debtor country introduces lower taxes than the non debtor one.

In addition, if the government in this country, thinking about its re-election, increases public spending then the country’s debt would end up even higher, since ∂P ξ ( β g − c ) − β ⎡⎣ z ( f + τ f ′ ) + ξ g ⎤⎦ = < 0. 2 ∂g ( β g − c)

100

(20)

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In this case, more taxes will be accompanied by increasing rates of change in the transaction cost: ∂ ( f + τ f ′) j ∂g j

=

1 ( β ⋅ Pj − ξ ) > 0 . zj

(21)

As a result, the total MU debt also increases, as shown from the shift from b0 to b1 , in Figure 6, triggering off a monetary policy tightening by the CCB (see equation (13)). A second order effect of such a tight policy is that inflation falls and total MU debt increases, moving the economy from point 1 to point 2 in Figure 6.

5.1.2

Case 1.2: Debtor country (i) introduces higher tax rates than the non-debtor one

In this case the government of the non debtor country j exploits its tax instrument’s efficiency which is related to low frictions and hence it enjoys a higher probability of reelection (i.e. a lower Pj). 20 This is portrayed in Figure 7.

Figure 7 bj z b ( bi )0 j j

bij ( bi )0

0

z (τ )

b jj ( bi )1 bij ( bi )1

1

2 b ( bi )2 i j

country j

b0 b1 b2 b jj ( bi )2

bi

country i τ

b

π

Notes: The path of the economy when the debtor country introduces higher taxes than the non debtor one.

20

This efficiency stems from the fact that its tax rates correspond to the “flat” area of the transaction cost function z, indicating a very low rate of change of the tax system transaction cost and, hence, an increase in its tax rate would result in relatively higher tax revenues due to the negligible rate of change of the transaction cost.

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Equation (19) suggests that any reduction in the probability Pj would shift the b jj (bi ) locus to the right (

∂CT j ∂Pj

< 0 ), from b jj (bi ) 0 to b jj (bi ) 1, resulting in a reduction of country j’s

debt level. On the other hand, the high frictions underlying country i’s tax policy are related to a higher transaction cost level and, consequently, to an inefficient tax instrument in reducing the country’s debt. Regarding country i, equation (18) implies that an increase in the country’s tax rates would cause country i’s government probability of no re-election to increase (

∂CTi >0) ∂Pi

and, hence, the bij (bi ) locus to shift to the right, from bij (bi ) 0 to bij (bi ) 1. This will increase the country’s debt level. This is depicted in Figure 7 by moving from the starting point 0 to point 1. This result is justified by the transaction cost approach that we develop in this paper. Total MU debt is reduced in this case, allowing for a looser monetary policy by the CCB (within the limits set by the level of inflation, e.g. π < 2% for the EMU). A change in inflation would affect the slope of the b jj (bi ) and bij (bi ) loci, since ∂ 2b θ (1 − γ ) ∂π 2 ∂slopei =− > 0, γ ∂π  2 i ⎛ ∂b ⎞ bt −1 ⎜ ⎟ ⎝ ∂π ⎠

and 2 γ j ∂ b (1 ) − δ b t −1 ∂slope j θ ∂π 2 < 0 . = ∂π ⎛ γ ∂b j ⎞ bt −1 ⎟ ⎜1 − ⎝ θ ∂π ⎠

The paths of each country’s debt levels and the total MU debt are portrayed in Figure 7.

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5.2

Scenario 2: Symmetric Countries, with respect to their Tax System’s Transaction Cost Function

The existence of symmetric transaction cost functions allows for strategic substitutability among countries.21 Specifically, when both countries face similar transaction cost functions, they also face cost functions with the same properties. This means that the countries are also similar regarding the effectiveness of their tax policies and that their governments have similar chances for re-election. Hence, unlike Scenario 1, here there is space for strategic behaviour. The outcome in the previous scenario was determined mainly by the constraints of the transaction cost, which were imposed on the effectiveness of fiscal policy by the tax systems. Technically, the symmetry of this scenario means that both countries lie within the same “area” along the transaction cost function and increase their tax rates within the same range. Next, we analyse this scenario for the following cases.

5.2.1

Case 2.1: Both countries choose tax rates which have a transaction cost with low rates of change

The increase in the tax rates of both countries in this case is consistent with a transaction cost which increases at a low rate as a result of an increase in tax rates. That is, fiscal authorities increase tax rates within the [ τ 0 ,τ 1 ] range in Figure 8. Regarding country i, recall that its debt level, bi , is initially above the reference value ( bi > b ). The fact that the transaction cost of the country’s tax system changes at a low rate makes it possible for the government to effectively use its tax instrument to reduce its debt level. This falls from bi0 to bi1 as a result of a backward shift of the bij (bi ) locus from bij (bi )0 to bij (bi )1 .22

21 22

See Bulow, Geanakoplos and Klemperer (1985), Beetsma, Debrun and Klaasen (2001).

∂CT j ∂CTi > 0, 0 ) and, hence, to a higher level of the transaction cost zj..25 This gives an ∂g j

23

Beetsma, Debrun and Klaasen (2001), Alesina (1990), Alesina and Tabellini (1987). It can be shown that there is no upper limit for gj. Note that this is not true in the following case, where an upper limit for the government’s public expenditure does exist. 25 Note that rearranging the optimality conditions results in zj being greater than a linear function of zi. 24

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additional reason for the increase in the country’s debt level, which is depicted in Figure 8 by a shift in the b jj (bi ) locus from bij (bi ) 0 to bij (bi ) 1. Total MU debt, b , increases, triggering off a tight monetary policy;26 the result is a lower inflation level. This creates second order effects on each country’s debt, as well as on total MU debt, which are pictured by a change in the slopes of the countries’ debt loci in Figure 8, moving the economy along the indicated trajectory to point 2. We should point out that the change in the slopes of the above loci reflects the effect of the Central Banker’s action on the behaviour of the countries. This is in line with the findings of Beetsma, Debrun and Klaasen (2001) and is indicative of the interaction between the monetary and public policies.

5.2.2

Case 2.2: Both countries choose tax rates which have a transaction cost with high rates of change

When the countries choose tax rates within the (τ1, 1] range, the transaction cost of their tax systems exhibits high rates of change as a result of an increase in their tax rates. The high debt level of country i ( bi > b ), in connection with the high transaction cost makes its tax instrument inefficient in reducing the country’s debt. The country’s debt level increases and so does society’s dissatisfaction (resulting in a higher probability of no reelection, Pi ). This is depicted by a shift in the bij (bi ) locus from bij (bi )0 to bij (bi )1 in Figure 9. 27 This increase in country i’s debt level could also be the result of strategic behaviour within the scenario of opportunistic behaviour by the party in office: having to face low chances of being elected again (high Pi), the government increases its public expenditure, despite the already high debt, as a means of increasing society’s satisfaction and, hence, its probability of re-election (

∂Pi < 0 ). ∂gi

26

The tight policy is justified by the optimality conditions, which require that

27

Recall that optimality indicates that

∂b θπ =− 0. ∂Pi

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However, this has second order effects as the higher public expenditure requires higher taxes, which need to be collected under the high transaction cost of the tax system (since

∂ ( f + τ f ′) > 0 ). As a result the country’s debt increases. On the other hand, from country ∂gi j’s point of view, the high rates of the transaction cost of its tax system, together with the resulting inefficiency of the tax instrument, indicate that it should adopt policies that counteract the financing implications of high tax rates. In other words, country j’s fiscal policy aims at public expenditure retrenchments, which negatively affect the rate of change of the transaction cost (

28

∂ ( f + τ f ′) > 0 ), ∂g j

smoothing the contribution of its tax instrument towards decreasing the country’s debt level. This country’s economic policy relies on “switching strategies”,29 in the sense that the government starts the fiscal consolidation by raising taxes and then moves into more politically sensitive policies, by reducing spending. With lower public spending society’s welfare decreases, resulting in a higher probability of no re-election, but at the same time the debt level also drops (since

∂CT j ∂Pj

< 0 ).

The reduction in country j’s debt is enough to drive down the total MU debt, leaving space for the Central Banker to loosen monetary policy.30 This affects the countries’ debt levels and total MU debt, which falls further as illustrated in Figure 9.

28

It can be shown that optimality requires zj < A+Bzi and gj < Γ+Δgi , where

A=

Γ=

ξ gi

( f + τ f ′) j

⋅

2 2 Pj b j Pj b j t −1 ⋅ ti−1 , B = 2 2 ⋅ i Pi bt −1 Pi bt −1

( f + τ f ′ )i ( f + τ f ′) j

,

Pj2 bt j−1 zi zj Pj2 bt j−1 zi ′ ′ f τ f f τ f and Δ = ⋅ ⋅ + − + ( )i ( )j ( f + τ f ′ )i . Pi 2 bti−1 ξ Pi 2 bti−1 ξ ξ

That is, optimality imposes an upper bound in country j’s public spending. 29 30

See, for example, OECD Economic Outlook 2007, and Von Hagen, Hughes and Strauch (2002).

 The monetary policy rule ∂b

∂π

< 0 implies that monetary loosening is consistent with reductions in the

slopes of the loci of the countries’ reaction functions.

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Figure 9

bj

z b jj ( bi )0

bij ( bi )0

z (τ )

b jj ( bi )2

0

b ( bi )2 i j

country i country j

2 1 τ0

bi b1 b2 bij ( bi )1

τ

τ1

b

b0

b jj ( bi )1

π

Notes: The path of the economy when both countries face transaction costs with high rates of change.

Summing up, the above analysis shows that there exists a channel, via the tax system’s transaction cost, that affects the CCB’s stabilisation policies. In other words, the optimal solution indicates a mechanism through which CCB policies targeting price stability are related to the fiscal policy variables of each MU country. The transaction cost of the tax system that we introduce into our analysis is an endogenous mechanism, which affects the effectiveness of fiscal policy instruments. Thus, we formally show a way in which the operational cost of the tax system of each MU member has inflationary consequences that depend on the characteristics of each individual country, as a token of fiscal policy non-neutrality.

6

Fiscal Rules vs Transaction Cost

In this section we focus on making inferences regarding the effectiveness of numerical fiscal rules we have modelled under the constraint implied by the existence of the transaction cost. It is worth noting that introducing this cost into our analysis affects the 107

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efficiency of the fiscal policy’s instrument endogenously. The endogenous mechanism relates the efficiency of fiscal policy (a quantitative result) to the frictions generated by the state–tax-payer interaction and which are related to behavioural issues. The latter are stipulated by economic, sociological and psychological characteristics, and tax administration aspects. With this in mind, we examine whether the numerical fiscal rule we introduce (see also Beetsma and Uhlig, 1999; and Debrun, 2007) affects the behaviour of the agents of our model. In terms of our analysis, we are interested in investigating whether the existence (or absence) of fiscal rules alters the slopes of the b jj (bi ) and bij (bi ) loci. Since the numerical

(

)

fiscal rules are expressed by the term δ b − b , where δ ∈ ( 0,1) , the case of a MU without fiscal rules corresponds to the case where δ = 0 . In this case, the b jj (bi ) and bij (bi ) loci become:

γ 1 1 − c − + b π ( ) j b jtj = + θ  γ ∂b j γ bt −1 1− 1− θ ∂π θ 1−

j t −1

∂b i bt −1 ∂π bti ,  ∂b j bt −1 ∂π

and

bijt =

1 − ci − (1 + π ) b γ ∂b i b θ ∂π t −1

i t −1

+

1−

γ ∂b i b θ ∂π t −1 bi t 

γ ∂b i b θ ∂π t −1

for country j and country i, respectively. The above loci retain the sign of their slopes, with

slope of b ij (bi ) < slope of b jj (bi ) indicating that the existence of numerical fiscal rules does not alter the countries’ strategic behaviour when the tax system’s transaction cost is explicitly modelled. A reasonable explanation for this is based on the micro-characteristics of the transaction cost: the tax system’s transaction cost relates the aspects of administration to the revenue losses that the government incurs due to the tax-payers’ behaviour, as a consequence of the existence of the tax system and governments’ tax policy. But the transaction cost, which is the cost underlying the state–tax-payers interaction, is related to the behaviour of tax-payers, who are not affected by the fiscal rules that underlie

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the government’s decision. This justifies the fact that, in terms of our model, numerical fiscal rules do not affect the slope of the reaction functions. This also corresponds to the way we have constructed the government’s objective function. In contrast to most theoretical work on economic policy issues, our study is not based on the assumption of the benevolent dictator government. This is because the notion of the transaction cost (i.e. the cost that evolves from the state–tax-payer interaction) distinguishes between the society (that pays taxes) and the government (that imposes taxes). This distinction makes it clear that the benevolent dictator assumption is not consistent with the government having identical preferences with the society; an assumption that would imply that there is no transaction cost.

7

Conclusion

In this paper we build a model in order to investigate monetary and fiscal policy interactions in the economic environment of a MU with two heterogeneous countries and a common central banker (CCB), who is conservative vis-à-vis inflation. Under this setting, we are looking for economic policy implications regarding the way that the efficiency of fiscal policy affects the price stability pursued by the CCB. The non-neutrality of fiscal policy implied by such a framework is consistent with a departure from the Ricardian Equivalence Proposition, whose acceptance is the stepping stone towards the view that inflation is only a monetary phenomenon. Theoretical work, consistent with the above mentioned “Ricardian Regime”, is based on the explicit assumption that the tax instrument does not have any effect on economic activity and, for that reason, a lump-sum or proportional taxation scheme prevails. Our analysis does not explicitly assume any specific type of tax instrument (e.g. lumpsum or proportional taxation). We cope instead, with a more general consideration of the tax system by introducing the tax system’s transaction or operation cost. This stems from the fact that, imposing taxes, generates frictions which are related to tax-payers’ behaviour, stipulated by socioeconomic and psychological characteristics, with tax administration aspects, like tax collection and tax compliance, resulting in the loss of tax revenue or deadweight loss (Feinstein 1998) with ultimate budgetary consequences. Thus, we have a microfountation of macroeconomic theory regarding monetary and fiscal policy interactions, where starting from the tax system’s operational properties, we 109

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are looking at the way the efficiency of fiscal policy is related to the political cycle, the path of debt and the level of inflation. Assuming heterogeneous countries enables us to identify possible spillovers in an interactive monetary and fiscal policy framework. We show that when we have a considerable degree of heterogeneity, the tax system’s transaction cost is the factor determining the countries’ policy choices and hence the resulting level of debt as well as the inflation path. On the other hand, when we have a considerable degree of homogeneity, it is the countries’ strategic behaviour that determines the outcome. We formally develop a channel, through which the operation of the tax system, related to the fiscal policy objectives is not independent of price stability which is the primary objective of the CCB. Under this framework, we also show that numerical fiscal rules are not efficient in altering the agents’ behaviour as they do not change the path of the economy.

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[25] Tabellini, G., and A. Alesina (1990). Voting on the Budget Deficit. American Economic Review, 80, 37-49. [26] Taylor, J. B. (1993). Discretion Versus Policy Rules in Practice. Carnegie-Rochester Conference Series on Public Policy, 39, 195-214. [27] Van Aarle, B., Bovenberg A. L., and M. G. Raith (1997). Is There a Tragedy of a Common Central Bank? A Dynamic Analysis. Journal of Economic Dynamics and Control, 21, 417-447. [28] Von Hagen, J., Hughes A., and R. Strauch (2001). Budgetary Consolidation in EMU. Directorate General Economic and Monetary Affairs, European Commission: European Economy - Economic Papers, 148. [29] Woodford, M. (2001). Fiscal Requirements for Price Stability. Journal of Money Credit and Banking, 33, 669-728. [30] Woodford, M. (2003). Interest and Prices. Princeton University Press.

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